On some peculiar aspects of the constructive theory of point-free spaces

Mathematical Logic Quarterly 56 (4):375-387 (2010)
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Abstract

This paper presents several independence results concerning the topos-valid and the intuitionistic predicative theory of locales. In particular, certain consequences of the consistency of a general form of Troelstra's uniformity principle with constructive set theory and type theory are examined

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10.1002/malq.200910037

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Citations of this work

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On the existence of Stone-Čech compactification.Giovanni Curi - 2010 - Journal of Symbolic Logic 75 (4):1137-1146.
Topological inductive definitions.Giovanni Curi - 2012 - Annals of Pure and Applied Logic 163 (11):1471-1483.

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References found in this work

Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Aspects of general topology in constructive set theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
Heyting-valued interpretations for constructive set theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.
Pretopologies and completeness proofs.Giovanni Sambin - 1995 - Journal of Symbolic Logic 60 (3):861-878.
CZF and second order arithmetic.Robert S. Lubarsky - 2006 - Annals of Pure and Applied Logic 141 (1):29-34.

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